At the Sigeman tournament, Fabiano Caruana, the Italian-American star who is ranked eighth in the world, grabbed the early lead by dispatching the struggling Anish Giri, the top player in the Netherlands, in the first round, and he defeated Hans Tikkanen, a Swedish grandmaster, in Round 2.

And in Cuba, Vassily Ivanchuk, who has won the last two Capablanca Memorial events — and has captured the tournament title five times — was leading by half a point after five rounds.

Such dominance by elite players is a bit unusual. Often, their well-prepared opponents can hold them to draws.

Nakamura surprised Hess in Round 1 by playing the Evans Gambit (4 b4), which was named after a 19th-century Welsh sea captain, who first played it in an 1827 game. It fell out of favor in the latter part of the last century until Garry Kasparov used it in 1995 to beat Viswanathan Anand at the Tal Memorial event in Riga, Latvia.

Though Hess said after the game that he had been unprepared for the gambit, he said he had lost because Nakamura “completely outplayed me.”

Hess had a reasonably good position after 9 Re1. To free his light-squared bishop, he could have played 9 ... b6 or even 9 ... Rb8, with the idea of continuing 10 ... b5. His 9 ... Ba3, which gave back the gambit pawn, was a mistake. He compounded that error by playing 10 ... Ne5, when 10 ... Bc1 11 Nc6 dc6 12 Qc1 h6 would have been better.

But Nakamura also made a mistake by playing 12 f4 instead of 12 Ba3. That move would have given him a bigger advantage after 12 ... Qa3 13 Nf3. Nakamura’s error gave Hess new life.

Hess got into new trouble with a few ill-advised moves, including 23 ... Re8, instead of 23 ... Qc7, as well as 26 ... Qb6, rather than 26 ... Rb5, and 27 ... Qb1, when he could have played 27 ... Rc7.

His final blunder was playing 28 ... Qa2 instead of 28 ... Rc7. That allowed Nakamura to spring a mating attack, beginning with 29 Be6. Hess resigned after 33 Qh7 because he could not stop mate.

A version of this article appeared in print on May 13, 2012, on page A18 of the New York edition with the headline: Fast Starts for Top Players At Three Elite Tournaments.